It is generally well known that undesirable eddy currents are induced in vacuum chambers that are used in particle beam accelerators. In such accelerators electro-magnets are positioned in operating relationship to a plurality of vacuum chambers through which charged particles are accelerated by an rf flux while being contained within a desired orbit by the flux fields produced by such positioning magnets. For those accelerators in which the magnetic fields of the particle beam-positioning magnets are rapidly cycled, it has been found that currents which are induced in the vacuum chambers as a consequence of such rapid cycling are a major source of both systematic and random aberrations in the magnetic fields of the particle beam accelerator lattice. It is possible to diminish the undesirable affect of such induced eddy currents by making the vacuum chamber walls relatively thin, but such thin walls are typically complex in structure and both expensive and delicate to handle. Such handling is extensive in applications where the vacuum chambers must undergo periodic vacuum-enhancing bakeouts. On the other hand, thick walled vacuum chambers for particle accelerator beams are desirably rugged and economical to construct and operate, but they have undesirably large eddy currents induced in them as a consequence of the particle beam-positioning magnets being rapidly cycled. In addition to the effects of different vacuum chamber walls thicknesses on the size of eddy currents induced in the chamber walls, it is known that random eddy current fields are also induced in such vacuum chamber walls due to variations in both geometrical and material tolerances, and due to variations in conductivity of the walls. In general, it has been found that such variations in the construction of vacuum chambers for particle accelerators dominate the induced aberrations in magnetic flux fields of typical rapid cycling particle accelerator lattices.